The government is set to weigh in on whether or not the Co-op will be allowed to build a new store in South Kirkby.
The supermarket wants to develop the town's old health centre on Barnsley Road, despite a petition of 134 signatures being tabled against the move.
Concerns have been raised about the proposed entrance to the Co-op's car park being "dangerous" and the potential impact on traffic around the site.
A decision on whether or not to approve the application was deferred at a July meeting, at which local councillor Steve Tulley called the plans the "worst I've seen in 40 years", on health and safety grounds.
Now the Co-op have complained to the government's Planning Inspectorate about the length of time taken to reach a decision.
Appeals can be made to the Planning Inspectorate (PI) if a decision is not made within eight weeks of an application being submitted.
Responding to the Co-op, the PI said an officer will visit the site as part of its own enquiries.
It added: "We are now waiting for a suitable planning inspector to become available.
"Once we are able to appoint an inspector you will be allocated a named case officer who will write to you starting the appeal and setting out details of the timetable and procedure.
"They will also confirm when the Inspector’s site visit/hearing will take place."
The Co-op declined to comment.